We propose a visual analytics approach for the exploration and analysis of dynamic networks. We consider snapshots of the network as points in high-dimensional space and project these to two dimensions for visualization and interaction using two juxtaposed views: one for showing a snapshot and one for showing the evolution of the network. With this approach users are enabled to detect stable states, recurring states, outlier topologies, and gain knowledge about the transitions between states and the network evolution in general. The components of our approach are discretization, vectorization and normalization, dimensionality reduction, and visualization and interaction, which are discussed in detail. The effectiveness of the approach is shown by applying it to artificial and real-world dynamic networks.

Networks are present in many fields such as finance, sociology, and transportation. Often these networks are dynamic: they have a structural as well as a temporal aspect. In addition to relations occurring over time, node information is frequently present such as hierarchical structure or time-series data. We present a technique that extends the Massive Sequence View ( msv) for the analysis of temporal and structural aspects of dynamic networks. Using features in the data as well as Gestalt principles in the visualization such as closure, proximity, and similarity, we developed node reordering strategies for the msv to make these features stand out that optionally take the hierarchical node structure into account. This enables users to find temporal properties such as trends, counter trends, periodicity, temporal shifts, and anomalies in the network as well as structural properties such as communities and stars. We introduce the circular msv that further reduces visual clutter. In addition, the (circular) msv is extended to also convey time-series data associated with the nodes. This enables users to analyze complex correlations between edge occurrence and node attribute changes. We show the effectiveness of the reordering methods on both synthetic and a rich real-world dynamic network data set.

Networks are present in many fields such as finance, sociology, and transportation. Often these networks are dynamic: they have a structural as well as a temporal aspect. We present a technique that extends the Massive Sequence View (MSV) for the analysis of the temporal and structural aspects of dynamic networks. Using features in the data as well as in the visualization based on the Gestalt principles closure, proximity, and similarity, we developed node reordering strategies for the MSV to make these features stand out. This enables users to find temporal properties such as trends, counter trends, periodicity, temporal shifts, and anomalies in the network as well as structural properties such as communities and stars. We show the effectiveness of the reordering methods on both synthetic and real-world transaction data sets.

We present the results of a study comparing five directed-edge representations for use in 2D, screen-based node-link diagrams. The goal of this work is to extend the understanding of tradeoffs and best practices for the representation of edges in directed graphs and to help practitioners choose among different options. Our work applies to graphs in which directed links are depicted using lines connecting the nodes. We tested five different edge representations chosen carefully based on user feedback to thoroughly cover the directed-edge design space. We also investigated how the use of pattern compression affects performance and subjective user preference. The article presents detailed results regarding the significant performance and preference differences between directed-edge representations and provides practical recommendations on their use.

Abstract Parallel coordinate plots (PCPs) are a well‐known visualization technique for viewing multivariate data. In the past, various visual modifications to PCPs have been proposed to facilitate tasks such as correlation and cluster identification, to reduce visual clutter, and to increase their information throughput. Most modifications pertain to the use of color and opacity, smooth curves, or the use of animation. Although many of these seem valid improvements, only few user studies have been performed to investigate this, especially with respect to cluster identification. We performed a user study to evaluate cluster identification performance – with respect to response time and correctness – of nine PCP variations, including standard PCPs. To generate the variations, we focused on covering existing techniques as well as possible while keeping testing feasible. This was done by adapting and merging techniques, which led to the following novel variations. The first is an effective way of embedding scatter plots into PCPs. The second is a technique for highlighting fuzzy clusters based on neighborhood density. The third is a spline‐based drawing technique to reduce ambiguity. The last is a pair of animation schemes for PCP rotation. We present an overview of the tested PCP variations and the results of our study. The most important result is that a fair number of the seemingly valid improvements, with the exception of scatter plots embedded into PCPs, do not result in significant performance gains.

A tanglegram is a pair of trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. In applications such as phylogenetics or hierarchical clustering, it is required that the individual trees are drawn crossing-free. A natural optimization problem, denoted tanglegram layout problem, is thus to minimize the number of crossings between inter-tree edges. The tanglegram layout problem is NP-hard even for complete binary trees, for general binary trees the problem is hard to approximate if the Unique Games Conjecture holds. In this paper we present an extensive experimental comparison of a new and several known heuristics for the general binary case. We measure the performance of the heuristics with a simple integer linear program and a new exact branch-and-bound algorithm. The new heuristic returns the first solution that the branch-and-bound algorithm computes (in quadratic time). Surprisingly, in most cases this simple heuristic is at least as good as the best of the other heuristics.

Graphs are often visualized using node-link representations: vertices are depicted as dots, edges are depicted as (poly)lines connecting two vertices. A directed edge running from vertex A to B is generally visualized using an arrow representation: a (poly)line with a triangular arrowhead at vertex B. Although this representation is intuitive, it is not guaranteed that a user is able to determine edge direction as quickly and unambiguously as possible; alternative representations that exhibit less occlusion and visual clutter might be better suited. To investigate this, we developed five additional directed-edge representations using combinations of shape and color. We performed a user study in which subjects performed different tasks on a collection of graphs using these representations and combinations thereof to investigate which representation is best in terms of speed and accuracy. We present our initial hypotheses, the outcome of the user studies, and recommendations regarding directed-edge visualization.

Abstract Graphs depicted as node‐link diagrams are widely used to show relationships between entities. However, node‐link diagrams comprised of a large number of nodes and edges often suffer from visual clutter. The use of edge bundling remedies this and reveals high‐level edge patterns. Previous methods require the graph to contain a hierarchy for this, or they construct a control mesh to guide the edge bundling process, which often results in bundles that show considerable variation in curvature along the overall bundle direction. We present a new edge bundling method that uses a self‐organizing approach to bundling in which edges are modeled as flexible springs that can attract each other. In contrast to previous methods, no hierarchy is used and no control mesh. The resulting bundled graphs show significant clutter reduction and clearly visible high‐level edge patterns. Curvature variation is furthermore minimized, resulting in smooth bundles that are easy to follow. Finally, we present a rendering technique that can be used to emphasize the bundling.

Abstract We provide a novel visualization method for the comparison of hierarchically organized data. Our technique visualizes a pair of hierarchies that are to be compared and simultaneously depicts how these hierarchies are related by explicitly visualizing the relations between matching subhierarchies. Elements that are unique to each hierarchy are shown, as well as the way in which hierarchy elements are relocated, split or joined. The relations between hierarchy elements are visualized using Hierarchical Edge Bundles (HEBs). HEBs reduce visual clutter, they visually emphasize the aforementioned splits, joins, and relocations of subhierarchies, and they provide an intuitive way in which users can interact with the relations. The focus throughout this paper is on the comparison of different versions of hierarchically organized software systems, but the technique is applicable to other kinds of hierarchical data as well. Various data sets of actual software systems are used to show how our technique can be employed to easily spot splits, joins, and relocations of elements, how sorting both hierarchies with respect to each other facilitates comparison tasks, and how user interaction is supported.

The use of dynamic information to aid in software understanding is a common practice nowadays. One of the many approaches concerns the comprehension of execution traces. A major issue in this context is scalability: due to the vast amounts of information, it is a very difficult task to successfully find your way through such traces without getting lost. In this paper, we propose the use of a novel trace visualization method based on a massive sequence and circular bundle view, constructed with scalability in mind. By means of three usage scenarios that were conducted on three different software systems, we show how our approach, implemented in a tool called EXTRAVIS, is applicable to the areas of trace exploration, feature location, and feature comprehension.

Color is routinely used to visualize interval and ordinal data, while texture is not. For color, a variety of perceptually based models is available, which can be used to convey data via straightforward mapping. The dimensionality of texture is less well understood and there are almost no perceptually based and validated models available to generate textures on demand. We present a perceptually based texture synthesis model for isotropic textures. The model uses additive synthesis of band-limited noise in the spectral domain, comparable to the RGB (red, green, blue) model for color. Via user experiments, we have derived a three-dimensional model to control the amplitudes per band in a perceptually intuitive way, comparable to the HSV (hue, saturation, value) model for color. The three dimensions used are contrast, spatial frequency, and spectral purity. Besides a mapping to the amplitudes, we have derived a mapping to a perceptually equidistant space. We show how such textures can be combined with color; applications are presented.

A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations.